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The purpose of this paper is to use an appropriate variational framework to discuss the boundary value problem with $p$-Laplacian type operators $$ \left\{\begin{array} {llcc} (\alpha(t,x^{\Delta}(t)))^{\Delta}-a(t)\phi_p(x^{\sigma}(t))+f(\sigma(t),x^{\sigma}(t))=0,~~\Delta{\text -\rm a.e.}~t\in I\nonumber\\ x^{\sigma}(0)=0,\nonumber\\\beta_1x^{\sigma}(1)+\beta_2x^{\Delta}(\sigma(1))=0, \end{array}\nonumber \right. $$ where $\beta_1,\beta_2>0$, $I=[0,1]^{k^2}$, $\alpha(\cdot,x(\cdot))$ is an operator of $p$-Laplacian type, $\mathbb{T}$ is a time scale. Some sufficient conditions for the existence of constant-sign solutions are obtained.
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참고문헌 (10)
참고문헌 신청
A. Cabada / 2005 / Criterions for absolute continuity on time scales / J. Difference Equ. Appl 11 (11) : 1013 ~ 1028
G. Cerami / 1979 / An existence criterion for the critical points on unbounded manifolds / Istit. Lombardo Accad. Sci. Lett. Rend. A 112 (2) : 332 ~ 336
J. Mawhin / 1989 / Critical Point Theorem and Hamiltonian Systems / Appl. Math. Sci 74
J. Simon / 1978 / R´egularit´e de la solution d’une ´equation non lin´eaire dans Rn, Journ´ees d’Analyse Non Lin´eaire (Proc. Conf., Besanon, 1977) / Lecture Notes i
L. Jiang / 2008 / Existence of weak solutions of two-point boundary value problems for second-order dynamic equations on time scales / Nonlinear Anal 69 (4) : 1376 ~ 1388
G. Cerami / 1979 / An existence criterion for the critical points on unbounded manifolds / Istit. Lombardo Accad. Sci. Lett. Rend. A 112 (2) : 332 ~ 336
J. Mawhin / 1989 / Critical Point Theorem and Hamiltonian Systems / Appl. Math. Sci 74
J. Simon / 1978 / R´egularit´e de la solution d’une ´equation non lin´eaire dans Rn, Journ´ees d’Analyse Non Lin´eaire (Proc. Conf., Besanon, 1977) / Lecture Notes i
L. Jiang / 2008 / Existence of weak solutions of two-point boundary value problems for second-order dynamic equations on time scales / Nonlinear Anal 69 (4) : 1376 ~ 1388
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